1. Field of the Invention
The invention relates generally to control schemes. In one embodiment, a system for optimizing a proportional, integral, derivative (PID) controller through the use of dynamic gains is disclosed.
2. Related Art
One of the major objectives of a biomechanical simulation tool is to determine the physiologically relevant muscle forces required for a given muscular-skeletal model performing a prescribed kinematic profile. Examples of kinematic profiles include the flexion of elbow or knee. However, kinematic profiles may also be more complex. For example, a kinematic profile may include the motion of walking. For many models and kinematic profiles there are multiple muscle activations that are possible. The goal of the simulation then becomes choosing the set of muscle activations, or muscle recruitment patterns, that best match what is expected for human motion. A typical assumption for this goal is the recruitment pattern that produces the minimum amount of muscle force while maintaining the kinematic profile and physiological limits. Other assumptions, or goals, are possible. For optimization, the problem being solved is a determination of the solution that best meets the desired muscle recruitment goal.
One solution approach used involves performing a static optimization. This approach directly optimizes muscle forces, within physiological limits, at sequential time steps via a quasi-dynamic, or static solution. Dynamic forward analysis, using the prescribed muscle force values, is then performed over some small time period during which the muscle forces are held constant prior to starting the next static solution.
There are two major limitations to this approach. First, it is based on sequential static solutions rather than a true dynamic solution. This has potential accuracy problems due to the limitation that the muscle forces are fixed over the time period between static solutions, rather than being a truly dynamically varying muscle force as would be the case with real muscles.
The second limitation is related to solution formulation. Since the static optimization formulation is a direct force optimization, there is not an opportunity to take advantage of a proportional-integral-derivative (PID) based force controller. The advantages of the PID control approach, namely solution stability and speed, are therefore given up in order to directly determine muscle forces through optimization.
Another solution approach involves using a PID control system for determining muscle force, with a separate PID controller for each muscle represented in the system. A classical PID control system uses proportional, integral, and derivative terms of an error function to generate a control signal which is fed back into the system. Typically each control term is multiplied by a constant gain that is set prior to running the system. Some biomechanical simulations of muscular-skeletal systems have used a PID control scheme, e.g. LifeMOD, for determining muscle forces required to meet a pre-determined kinematic profile. This is done by using a sensor of the muscle kinematics, e.g. muscle length, muscle velocity, or joint angle, which is compared to a target signal. Output of the control system is a muscle control force that may further be modified to physiological limitations based on maximum force, velocity, etc.
The PID control scheme is an efficient and stable approach for determining muscle forces in a model required to meet the prescribed kinematic profile. For situations where multiple muscle activations, or recruitment patterns, are able to meet the same kinematic profile, however, the approach does not preferentially choose the solution that has the minimum force, or any other assumed recruitment objective. Thus, an improved system for determining muscle forces in a model is desirable.